Solve for $m$. $\dfrac m{9}+\dfrac23=\dfrac73 $
Answer: Let's subtract and then multiply to get $m$ by itself. $\begin{aligned} \dfrac m{9}+\dfrac23&=\dfrac73 \\ \\ \dfrac m{9}+\dfrac23{-\dfrac23} &=\dfrac73{-\dfrac23}~~~~~{\text{subtract }\dfrac23} \text{ from each side}\\ \\ \dfrac m9+\cancel{\dfrac23} {{-}\cancel{{\dfrac23}}}&= \dfrac73{ -\dfrac23}\\ \\ \dfrac m{9}&= \dfrac73{-\dfrac23}\end{aligned}$ $\begin{aligned}\dfrac m9&= \dfrac53 \\ \\ \dfrac m{9}\cdot{{9}}&= \dfrac{5}3\cdot{{9}} ~~~~~~~\text{multiply each side by } {9} \text{ to get } m \text{ by itself }\\ \\ \dfrac m{\cancel{9}}\cdot{\cancel{{9}}} &=\dfrac{5}3\cdot{{9}} \\ \\ m&= {\dfrac53}\cdot{{9}} \\\\ m&= {\dfrac{45}3}\end{aligned}$ The answer: $m={15}$ Let's check to make sure. $\begin{aligned} \dfrac m{9}+\dfrac23&=\dfrac73 \\\\ \dfrac{{15}}{9}+\dfrac23&\stackrel{?}{=} \dfrac73 \\\\ \dfrac53+\dfrac23&\stackrel{?}{=} \dfrac73 \\\\ \dfrac73&= \dfrac73 ~~~~~~~~~~\text{Yes!} \end{aligned}$